Many important optical materials exhibit birefringence. Birefringence causes different linear polarizations of light to travel at different speeds through the material. These different polarizations are most often considered as two components of the polarized light, one component being orthogonal to the other.
Birefringence is an intrinsic property of many optical materials, and may also be induced by external forces applied to the material. The induced birefringence may be temporary, as when the material is oscillated, or the birefringence may be residual, as may happen when, for example, the material undergoes thermal stress during production of the material.
Retardation or retardance represents the integrated effect of birefringence acting along the path of a light beam that traverses a sample of the optical material. If the incident light beam is linearly polarized, the two orthogonal components of the polarized light will exit the sample with a phase difference, called the retardance. The fundamental unit of retardance is length, such as nanometers (nm). It is frequently convenient, however, to express retardance in units of phase angle (waves, radians, or degrees), which is proportional to the retardance (nm) divided by the wavelength of the light (nm). An “average” birefringence for a sample is sometimes computed by dividing the measured retardation magnitude by the thickness of the sample.
The two orthogonal, polarized beam components mentioned above are parallel to two orthogonal axes associated with the optical material, which axes are referred to as the “fast axis” and the “slow axis.” The fast axis is the axis of the material that aligns with the faster moving component of the polarized light through the sample. Therefore, a complete description of the retardance of a sample along a given optical path requires specifying both the magnitude of the retardance and the relative angular orientation of the fast (or slow) axis of the sample.
The need for precise measurement of birefringence properties has become increasingly important in a number of technical applications. For instance, it is important to specify linear birefringence in optical elements that are used in high-precision instruments employed in semiconductor and other industries.
The prior art, including U.S. Pat. No. 6,473,747, Birefringence Measurement System, hereby incorporated by reference, discloses methods and apparatus for measuring birefringence of a sample using a light beam that is directed through the sample at a normal (zero-degree) incidence angle relative to the surface of the sample. As a result, the determination of the sample's birefringence is “in-plane,” meaning that the determination essentially represents the difference between the indices of refraction of two orthogonal axes in a plane of the sample, that plane being normal to the incident light beam.
The effect of birefringence on displayed visible light (such effects occurring, for example, when the light passes through an optical film or coating) may be to reduce contrast or alter colors. Also, with many materials, such as those used with liquid crystal display (LCD) panels, the extent or magnitude of birefringence is a function of the incident angle of the light under consideration. For example, increasing (from normal) the viewing angle of a LCD panel will increase the birefringence effect on the light emanating from the panel and, without compensation, reduce the perceived quality of the visible light by reducing contrast and/or altering colors.
Transparent polymer films have been developed for use with LCD panels for the purpose of compensating for the just-noted birefringence variations attributable to viewing angle. In short, these films possess birefringence characteristics that compensate for the birefringence of the LCD panel and thus provide a wide viewing angle without significant loss of contrast or color.
It is important to properly characterize the birefringence of such films, and other optical materials, in planes that are parallel to the normal (zero-degree) angle of incidence. This birefringence measure can be referred to as “vertical” or “out-of-plane” birefringence. One can consider the notion of in-plane and out-of-plane birefringence in terms of a Cartesian coordinate system. Accordingly, if the normal-incidence light is considered to travel in a direction parallel to the Z-axis of such a coordinate system, the in-plane birefringence occurs in the XY plane of the sample. Out-of-plane birefringence is in a plane perpendicular to the in-plane birefringence, thus occurring in the XZ or YZ plane.
Other applications (in additional to the birefringence compensation film example just discussed) may call for precise determination of out-of-plane birefringence. For example, certain cubic crystals, such as calcium fluoride, may exhibit intrinsic birefringence when short-wavelength light (for example, 157 nm) propagates through the crystal. The intrinsic birefringence is greatest between the [001] and [110] axes of the crystal. Also, such crystals are often produced with an outer surface or “window” for receiving incident light normal to the [111] surfaces of the crystal. As a result, the just mentioned intrinsic birefringence present between the [001] and [110] axes of the crystal is out-of-plane birefringence relative to the light that is normal to the [111] surface. The difference with the Cartesian corrdinate anoalogy mentioned in the prior paragraph is that the [111] axis is not normal to the [110] or [001] axes. Nevertheless, it is still amenable to the measurement techniques of the present invention as summarized next.